Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587593 | C2 | semidirect |
| 3. #11762886 | C2 | semidirect |
| 4. #11762874 | C2 | semidirect |
| 5. #11762777 | C2 | semidirect |
| 6. C2×C4×#3622 | C2 | semidirect |
| 7. C17×#423 | C2 | semidirect |
| 42. C2×#3622 | D4 | semidirect |
| 76. C4×C17 | #131 | semidirect |
| 84. #423 | D17 | semidirect |
| 108. C17 | #2931 | semidirect |
| 160. C4 | #10587593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587593 | 2 |
| #11763359 | 2 |
| #11762886 | 2 |
| #11762874 | 2 |
| #11762777 | 2 |
| C2×C4×#3622 | 2 |
| C17×#423 | 2 |
| #2931 | 17 |